Topic Check In - 3.01 Powers and roots
Write the following in index form, as simply as possible.
1. 3 × 3 × 3 × 3 × 3
2. 52 × 57
3. 86 ÷ 82
Calculate the following.
4.
5.
36
3
64
6. Explain why 83 is greater than 8 × 3.
7. Explain why 52 + 62 is not equal to 112.
8. Given that the volume of a cube is found using the formula V = s3, show how to find
the length of the sides, s, for a cube with volume of 27 cm3.
9. x2 + y = 37, x + y2 = 149. Calculate the values of x and y.
10. Find the value of a and the value of b given that 2a + 3b = 82.
Extension
a) 21 = 2, 22 = 4, 23 = 8
Find the least value of n where 2n > 5000.
b) 31 = 3, 32 = 9, 33 = 27
Find the least value of n where 3n > 5000.
c) Find different pairs of values for m and n when m > n and mn > 5000.
Answers
1.
35
2.
59
3. 84
4.
±6
5. 4
6. 83 means 8 × 8 × 8 = 512 which is greater than 8 × 3 = 24
7. Must do the indices before the addition 25 + 36 = 61, 112 = 121 so 52 + 62 ≠ (5 + 6)2
8.
3
9.
x = 5, y = 12
27 = 3 cm
10. a = 0, b = 4
Extension
a) 213 = 8192
b) 38 = 6561
c) Possible solutions:
m
n
mn
6
5
7776
7
5
16807
8
5
32768
9
4
6561
10
4
10000
18
3
5832
71
2
5041
5001
1
5001
We’d like to know your view on the resources we produce. By clicking on the ‘Like’ or ‘Dislike’
button you can help us to ensure that our resources work for you. When the email template pops
up please add additional comments if you wish and then just click ‘Send’. Thank you.
If you do not currently offer this OCR qualification but would like to do so, please complete the
Expression of Interest Form which can be found here: www.ocr.org.uk/expression-of-interest
OCR Resources: the small print
OCR’s resources are provided to support the teaching of OCR specifications, but in no way constitute an endorsed teaching method that is required by the Board,
and the decision to use them lies with the individual teacher. Whilst every effort is made to ensure the accuracy of the content, OCR cannot be held responsible for
any errors or omissions within these resources. We update our resources on a regular basis, so please check the OCR website to ensure you have the most up to
date version.
© OCR 2015 - This resource may be freely copied and distributed, as long as the OCR logo and this message remain intact and OCR is acknowledged as the
originator of this work.
OCR acknowledges the use of the following content: Maths and English icons: Air0ne/Shutterstock.com. Thumbs up and down icons: alexwhite/Shutterstock.com
Please get in touch if you want to discuss the accessibility of resources we offer to support delivery of our qualifications: resources.feedback@ocr.org.uk
Assessment
Objective
Qu.
Topic
R
A
G
Assessment
Objective
Qu.
Topic
AO1
1
Write expressions in index form.
AO1
1
Write expressions in index form.
AO1
2
Multiply expressions written in index form.
AO1
2
Multiply expressions written in index form.
AO1
3
Divide expressions written in index form.
AO1
3
Divide expressions written in index form.
AO1
4
Calculate simple square roots.
AO1
4
Calculate simple square roots.
AO1
5
Calculate simple cube roots.
AO1
5
Calculate simple cube roots.
AO2
6
Understand the meaning of index notation.
AO2
6
Understand the meaning of index notation.
AO2
7
AO2
7
AO2
8
AO2
8
AO3
9
Solve problems involving indices.
AO3
9
Solve problems involving indices.
AO3
10
Apply index rules in solving problems.
AO3
10
Apply index rules in solving problems.
Assessment
Qu.
Assessment
Qu.
Objective
Justify the correct order of operations with indices
(BIDMAS).
Clearly apply rules of powers and roots in the context of
volume.
Topic
R
A
G
Objective
Topic
1
Write expressions in index form.
AO1
1
Write expressions in index form.
AO1
2
Multiply expressions written in index form.
AO1
2
Multiply expressions written in index form.
AO1
3
Divide expressions written in index form.
AO1
3
Divide expressions written in index form.
AO1
4
Calculate simple square roots.
AO1
4
Calculate simple square roots.
AO1
5
Calculate simple cube roots.
AO1
5
Calculate simple cube roots.
AO2
6
Understand the meaning of index notation.
AO2
6
AO2
7
AO2
8
AO3
9
AO3
10
A
G
R
A
G
Justify the correct order of operations with indices
(BIDMAS).
Clearly apply rules of powers and roots in the context of
volume.
AO1
Justify the correct order of operations with indices
(BIDMAS).
Clearly apply rules of powers and roots in the context of
volume.
R
Understand the meaning of index notation.
Justify the correct order of operations with indices
(BIDMAS).
Clearly apply rules of powers and roots in the context of
volume.
AO2
7
AO2
8
Solve problems involving indices.
AO3
9
Solve problems involving indices.
Apply index rules in solving problems.
AO3
10
Apply index rules in solving problems.